A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.

A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (Fig. P7.8). A drop that breaks loose from the tire on one turn rises vertically 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The radius of the wheel is 0.381 m. (a) Why does the first drop rise higher than the second drop? (b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheels angular acceleration (assuming it to be constant). Figure P7.8 Problems 8 and 69.

Which rolls down an inclined plane faster, a hollow cylinder or a solid sphere? Both have the same mass and radius.

A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?

What if another planet the same size as Earth were put into orbit around the Sun along with Earth. Would the moment of inertia of the system increase, decrease, or stay the same?

Circular orbits in Equation 13.10 for conic sections must have eccentricity zero. From this, and using Newton’s second law applied to centripeta acceleration, show that the value of in Equation 13.10 is given by Where is the angular momentum of the orbiting body. The value of is constant and given by this expression regardless of the type of orbit.

An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is 1.8kgm2 while his arms are extended, and he is spinning at 0.5 rev/s. If he launches himself into the air at 9.0 m/s at an angle of 45 with respect to the ice, how many revolutions can he execute while airborne if his moment of inertia in the air is 0.5kgm2 ?

A buzzard (m = 9.29 kg) is flying in circular motion with aspeed of 8.44 m/s while viewing its meal below. If the radius ofthe buzzards circular motion is 8.00 m, what is the angularmomentum of the buzzardaround the center of its motion?

A Ferris wheel turns at a constant 170.0 revolutions per hour. (a)   Express this rate of rotation in units of radians per second.   (b)   If the wheel has a radius of 11.0 m, what arc length does a passenger trace out during a ride lasting 5.05 min?   (c)   If the wheel then slows to rest in 9.66 s while making a quarter turn, calculate the magnitude of its average angular speed during that time.